You place a pencil in front of a concave lens with a focal length of . The magnification of the image is $m=\frac{1}{2}$. If you wanted to make the image even smaller, should you move the pencil closer to the lens or farther away?

• A. Closer
• B. Farther
• C. Neither

Answer: (B)

Verified step by step guidance

1. Recall the lens formula relating object distance (d_o), image distance (d_i), and focal length (f): \(\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}\).
2. Recall the magnification formula for lenses: \(m = \frac{d_i}{d_o}\), where magnification (m) is the ratio of image height to object height.
3. Since the lens is concave, the focal length \(f\) is negative, and the image formed is virtual, upright, and reduced in size, so \(m\) is positive but less than 1.
4. To make the image smaller (reduce magnification), analyze how changing the object distance \(d_o\) affects \(m = \frac{d_i}{d_o}\) using the lens formula to express \(d_i\) in terms of \(d_o\) and \(f\).
5. By increasing the object distance (moving the pencil farther from the lens), the image distance \(d_i\) changes such that the magnification \(m\) decreases, making the image smaller.